A switch has a 0.9 probability of working effectively. If it does work, then the probability remains the same on the next occasion that it is used. If, however, it does not work effectively, then the probability it works on the next occasion is 0.1. Use a tree diagram to find the probability:
a. It works on three successive occasions;
b. It fails, but then works on the next two occasions;
c. On four occasions it works, fails, works and then fails.